基于加权压缩感知的MR图像重建方法

背景：压缩感知理论已广泛应用于MR图像的快速重建中。在对K空间数据进行随机欠采样后,通过非线性优化算法求解带约束的范数最小化问题,可恢复出在变换域具有稀疏性的MR图像。 目的：为了增强图像在变换域中的稀疏性,改善MR图像重建质量,提出了对待重建图像的稀疏表示进行加权的方法。 方法：采用非线性共轭梯度下降算法求解该加权范数最小化问题,在迭代过程中,根据所求取的图像稀疏表示来更新权值矩阵,增强MR图像的稀疏性。 结果与结论：通过比较带加权矩阵和不带加权矩阵的压缩感知图像重建方法,结果表明带加权矩阵改进的算法提高了图像重建能力。

Magnetic resonance image reconstruction based on weighted compressed sensing

BACKGROUND:Compressed sensing theory is widely used in the fast reconstruction of magnetic resonance image (MRI). According to randomly undersampling the k-space data, MRI with sparsity in the transform domain can be reconstructed exactly and this can be done by solving the constrained minimization problems using non-linear optimization algorithm. OBJECTIVE:To enhance the sparsity of the image in transform domain and improve the quality of MRI econstruction, a new approach to weight the sparse presentation of the image is proposed in this paper. METHODS:The nonlinear conjugate-gradient descent algorithm was utilized to solve the weighted norm minimization. In each iteration, according to the acquired image’s sparse presentation, weighted matrix was updated to enhance the sparsity of MRI. RESULTS AND CONCLUSION:Several experiments were carried out with and without reweighting the norm. Results demonstrate that the proposed algorithm with weighted matrix can obviously improve the ability of image recovery.